On the basis theorem for differential systems

Autor:	E. R. Kolchin
Rok vydání:	1942
Předmět:	Pure mathematics Factor theorem Arzelà–Ascoli theorem Fundamental theorem Picard–Lindelöf theorem Applied Mathematics General Mathematics Compactness theorem Mathematical analysis Fixed-point theorem Brouwer fixed-point theorem Mathematics Peano existence theorem
Zdroj:	Transactions of the American Mathematical Society. 52:115-127
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-1942-0006164-4
Popis:	As originally proved by Hilbert, this theorem applied to polynomials whose coefficients were either elements of a field, or rational integers. In keeping with the modern tendency toward abstraction, however, one now finds the theorem proved for polynomials whose coefficients are elements of a commutative ring with unit element in which every set has a finite basis. When one turns to differential polynomials and differential ideals one finds that the exact analogue of the Hilbert theorem is lacking('). It is not true that every system of differential polynomials z contains a finite subset F1, * *, F8 such that
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c505a8156296b2ada6a9e2f30e26e896 https://doi.org/10.1090/s0002-9947-1942-0006164-4 Zobrazit plný text záznamu